Laguerre functions on symmetric cones and recursion relations in the real case Academic Article

abstract

• In this article we derive differential recursion relations for the Laguerre functions on the cone C of positive definite real matrices. The highest weight representations of the group Sp(n,R) play a fundamental role. Each such representation acts on a Hilbert space of holomorphic functions on the tube domain C+ i Sym(n,R). We then use the Laplace transform to carry the Lie algebra action over to L^2(C ,dm_t). The differential recursion relations result by restricting to a distinguished three dimensional subalgebra, which is isomorphic to sl(2,R).

authors

• Aristidou, Michael

published proceedings

• JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

author list (cited authors)

• Aristidou, M., Davidson, M., & Olafsson, G.

citation count

• 4

complete list of authors

• Aristidou, Michael||Davidson, Mark||Olafsson, Gestur

publication date

• February 2007

publisher

• Elsevier  Publisher

published in

• Journal of Computational and Applied Mathematics  Journal

keywords

• Highest Weight Representations
• Lagurre Functions And Polynomials
• Recursion Relations
• Symmetric Matrics
• Tube Type Domains

Digital Object Identifier (DOI)

• 10.1016/j.cam.2005.12.002

start page

• 95

end page

• 112

volume

• 199

issue

• 1

URL

• http://dx.doi.org/10.1016/j.cam.2005.12.002